A simple answer:
sa - single action, the hammer must be cocked each time in order to fire the weapon. i.e Ruger Blackhawk, Colt Peacemaker
da - double action, weapon can be fired by simply pulling the trigger on the first and suceeding shots. In a revolver the trigger pull cocks and releases the hammer (Colt Python, S&W 19, etc.) and on a DA pistol, after the first shot the hammer is cocked during the cycling of the action (Beretta 92, Taurus 92, etc.).
DAO - double action only, pistols with this type of action are shot each time with the hammer being cocked and released with each shot. The hammer, if it is exposed, cannot be cocked manually. A few models have some extremely nice triggers for DAO. (S&W, Springfield)